"Spherical Geometry" is an article from The American Mathematical Monthly, Volume 11 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2970342
Source: http://www.jstor.org/stable/10.2307/2970342
"Spherical Geometry" is an article from The American Mathematical Monthly, Volume 11 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2970130
Source: http://www.jstor.org/stable/10.2307/2970130
"Spherical Geometry" is an article from The American Mathematical Monthly, Volume 11 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2967867
Source: http://www.jstor.org/stable/10.2307/2967867
"Spherical Geometry" is an article from The American Mathematical Monthly, Volume 11 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2969011
Source: http://www.jstor.org/stable/10.2307/2969011
"Spherical Geometry" is an article from The American Mathematical Monthly, Volume 11 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2970746
Source: http://www.jstor.org/stable/10.2307/2970746
"Spherical Geometry" is an article from The American Mathematical Monthly, Volume 11 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2968842
Source: http://www.jstor.org/stable/10.2307/2968842
"Spherical Geometry" is an article from The American Mathematical Monthly, Volume 11 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2970518
Source: http://www.jstor.org/stable/10.2307/2970518
"Note on Spherical Geometry" is an article from The American Mathematical Monthly, Volume 6 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2969675
Source: http://www.jstor.org/stable/10.2307/2969675
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161
Jan 21, 2017
01/17
by
Leighton,henry,l.g
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Book Source: Digital Library of India Item 2015.212074 dc.contributor.author: Leighton,henry,l.g dc.date.accessioned: 2015-07-09T17:48:01Z dc.date.available: 2015-07-09T17:48:01Z dc.date.digitalpublicationdate: 2005-02-20 dc.date.citation: 1943 dc.identifier.barcode: 1040010080781 dc.identifier.origpath: /data_copy/upload/0080/786 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/212074 dc.description.scannerno: 2 dc.description.scanningcentre: IISc, Bangalore...
Topic: Other
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236
Jan 24, 2017
01/17
by
Hart,william,l
texts
eye 236
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Book Source: Digital Library of India Item 2015.212075 dc.contributor.author: Hart,walter,w dc.contributor.author: Hart,william,l dc.date.accessioned: 2015-07-09T17:48:02Z dc.date.available: 2015-07-09T17:48:02Z dc.date.digitalpublicationdate: 2005-01-12 dc.date.citation: 1942 dc.identifier.barcode: 1040010080782 dc.identifier.origpath: /data_copy/upload/0080/787 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/212075 dc.description.scannerno: 2...
Topic: Other
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70
Sep 24, 2013
09/13
by
Pierre-François Loos
texts
eye 70
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Using the spherical geometry, we introduce a novel model to study excitons confined in a three-dimensional space, which offers unparalleled mathematical simplicity while retaining much of the key physics. This new model consists of an exciton trapped on the 3-sphere (i.e. the surface of a four-dimensional ball), and provides a unified treatment of Frenkel and Wannier-Mott excitons. Moreover, we show that one can determine, for particular values of the dielectric constant $\epsilon$, the...
Source: http://arxiv.org/abs/1112.5313v3
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81
Sep 18, 2013
09/13
by
Nicolas Perrin
texts
eye 81
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Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
Source: http://arxiv.org/abs/1211.1277v1
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10.0
Jun 28, 2018
06/18
by
Yashar Memarian
texts
eye 10
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Spherical localisation is a technique whose history goes back to M.Gromov and V.Milman. It's counterpart, the Euclidean localisation is extensively studied and has been put to great use in various branches of mathematics. The purpose of this paper is to quickly introduce spherical localisation, as well as demonstrate some of its applications in convex and metric geometry.
Topics: Metric Geometry, Mathematics
Source: http://arxiv.org/abs/1507.00915
Title from cover
Topic: NAVIGATION.EARTH MODELS.ALGORITHMS.
"Geometry Within a Linear Spherical Complex" is an article from Transactions of the American Mathematical Society, Volume 2 . View more articles from Transactions of the American Mathematical Society . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-1986207
Source: http://www.jstor.org/stable/10.2307/1986207
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40
Sep 21, 2013
09/13
by
Xing Wei; Andreas Tilgner
texts
eye 40
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We investigate numerically in spherical geometry the interaction of stratification with precession. Both stable stratification and unstable stratification are studied. In the parameter regime we are concerned with, stable stratification suppresses the precessional instability, whereas unstable stratification and precession can either stablise or destablise each other at the different precession rates.
Source: http://arxiv.org/abs/1301.6881v2
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21
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eye 21
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24
texts
eye 24
favorite 0
comment 0
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35
Sep 19, 2013
09/13
by
P. J. Käpylä; M. J. Korpi; A. Brandenburg; D. Mitra; R. Tavakol
texts
eye 35
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Self-consistent convective dynamo simulations in wedge-shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large-scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made.
Source: http://arxiv.org/abs/0909.1330v3
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34
Sep 18, 2013
09/13
by
W. Janke; D. A. Johnston; R. Kenna
texts
eye 34
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Motivated by previous observations that geometrizing statistical mechanics offers an interesting alternative to more standard approaches,we have recently calculated the curvature (the fundamental object in this approach) of the information geometry metric for the Ising model on an ensemble of planar random graphs. The standard critical exponents for this model are alpha=-1, beta=1/2, gamma=2 and we found that the scalar curvature, R, behaves as epsilon^(-2),where epsilon = beta_c - beta is the...
Source: http://arxiv.org/abs/cond-mat/0210571v1
1
1.0
Jun 30, 2018
06/18
by
Florian Besau; Franz E. Schuster
texts
eye 1
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Characterizations of binary operations between convex bodies on the Euclidean unit sphere are established. The main result shows that the convex hull is essentially the only non-trivial projection covariant operation between pairs of convex bodies contained in open hemispheres. Moreover, it is proved that any continuous and projection covariant binary operation between all proper spherical convex bodies must be trivial.
Topics: Mathematics, Metric Geometry
Source: http://arxiv.org/abs/1407.1153
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36
Sep 22, 2013
09/13
by
Basudeb Dasgupta; Amol Dighe; Alessandro Mirizzi; Georg G. Raffelt
texts
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The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the non-spherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the...
Source: http://arxiv.org/abs/0805.3300v1
1
1.0
Jun 30, 2018
06/18
by
Athanase Papadopoulos; Weixu Su
texts
eye 1
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We provide hyperbolic analogues of some classical theorems in spherical geometry due to Menelaus, Euler, Lexell, Ceva and Lambert. Some of the spherical results are also made more precise.
Topics: Mathematics, Metric Geometry, Geometric Topology
Source: http://arxiv.org/abs/1409.4742
3
3.0
Jun 29, 2018
06/18
by
Maurizia Rossi
texts
eye 3
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In this PhD Thesis we investigate the geometry of random fields on compact Riemannian manifolds, in particular the two-dimensional sphere. In the first part, we characterize isotropic Gaussian fields on homogeneous spaces of a compact group and then we prove the non-existence of P. L\'evy's Brownian field on the group SO(3), which moreover allows to extend the same kind of result to SO(n), SU(n) for n bigger than 3. In the second part, we investigate the high-energy behavior of random...
Topics: Probability, Mathematical Physics, Mathematics
Source: http://arxiv.org/abs/1603.07575
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20
Sep 22, 2013
09/13
by
Thomas Kvorning
texts
eye 20
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Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until now, the constructions have been restricted to flat geometries, but in this paper we generalize to the simplest curved geometry, namely that of a sphere. Except for being of interest for numerical studies, that usually are performed on a sphere, the response of...
Source: http://arxiv.org/abs/1302.3808v2
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31
Sep 23, 2013
09/13
by
Yan Li; Fu-Lin Zhang; Jing-Ling Chen
texts
eye 31
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The Virial Theorem in the one- and two-dimensional spherical geometry are presented, in both classical and quantum mechanics. Choosing a special class of Hypervirial operators, the quantum Hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman Theorem, these relations can be used to formulate a \emph{perturbation theorem without wave functions}, corresponding to the Hypervirial-Hellmann-Feynman Theorem perturbation theorem of Euclidean geometry. The...
Source: http://arxiv.org/abs/1012.5391v2
709
709
Sep 13, 2008
09/08
by
William Frothingham Bradbury
texts
eye 709
favorite 1
comment 0
Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.
Topics: equal, angle, angles, triangle, plane, sides, perpendicular, triangles, theorem, parallel, equally...
Source: http://books.google.com/books?id=NyQAAAAAYAAJ&oe=UTF-8
This report presents two great circle navigation algorithms, a closest point of approach algorithm and intercept algorithm. It also presents an implementation program for the algorithms that is written in the BASIC language for an IBM PC. Instead of using classical spherical geometry or the general spherical triangle, these algorithms incorporate rectangular coordinates and vectors on the surface of the spherical. The intent of the report is to provide algorithms for spherical earth models that...
Topics: DTIC Archive, Shudde, Rex H., NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *ALGORITHMS, *NAVIGATION,...
48
48
Oct 8, 2015
10/15
by
Shudde, Rex H.
texts
eye 48
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comment 0
Title from cover
Topic: NAVIGATION.EARTH MODELS.ALGORITHMS.
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48
Sep 18, 2013
09/13
by
N. A. Gromov
texts
eye 48
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A new formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The free Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same fields with the same masses as the Standard Electroweak Model. The vector bosons and electron masses are generated automatically, so there is no need in special mechanism.
Source: http://arxiv.org/abs/0705.4575v1
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678
Apr 27, 2008
04/08
by
William Chauvenet
texts
eye 678
favorite 0
comment 0
Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.
Topics: sin, tan, log, cos, cot, tlie, angle, spherical, angles, log sin, log tan, google solution, log...
Source: http://books.google.com/books?id=15ZhadfW-yUC&oe=UTF-8
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91
Sep 23, 2013
09/13
by
M. J. W. Dodgson; M. A. Moore
texts
eye 91
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We report results from Monte Carlo simulations of a thin film superconductor in a spherical geometry within the lowest Landau level approximation. We observe the absence of a phase transition to a low temperature vortex solid phase with these boundary conditions; the system remains in the vortex liquid phase for all accessible temperatures. The correlation lengths are measured for phase coherence and density modulation. Both lengths display identical temperature dependences, with an asymptotic...
Source: http://arxiv.org/abs/cond-mat/9512123v2
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31
Sep 21, 2013
09/13
by
Johann Kronthaler
texts
eye 31
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comment 0
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data, which is smooth and compactly supported outside the event horizon.
Source: http://arxiv.org/abs/0709.3703v1
"On the Application of Analysis to Spherical Geometry" is an article from Proceedings of the Royal Irish Academy (1836-1869), Volume 2 . View more articles from Proceedings of the Royal Irish Academy (1836-1869) . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-20520075
Source: http://www.jstor.org/stable/10.2307/20520075
A method of solution for the equation of radiative transfer for a spherical, grey atmosphere, steady state plasma in radiative equilibrium is developed. The method is called the ray integration technique and derives from the same method of solution done in cylinder geometry at Los Alamos National Laboratory. The total and net radiation flux, source function opacity and moments of intensity are calculated as a function of radius. The solution to the zero'th and first moment equations are also...
Topics: DTIC Archive, Durham,Susan E, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING,...
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73
Sep 22, 2013
09/13
by
Akira Kageyama; Tetsuya Sato
texts
eye 73
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A new kind of overset grid, named Yin-Yang grid, for spherical geometry is proposed. The Yin-Yang grid is composed of two identical component grids that are combined in a complemental way to cover a spherical surface with partial overlap on their boundaries. Each component grid is a low latitude part of the latitude-longitude grid. Therefore the grid spacing is quasi-uniform and the metric tensors are simple and analytically known. One can directly apply mathematical and numerical resources...
Source: http://arxiv.org/abs/physics/0403123v1
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25
Sep 18, 2013
09/13
by
Frans Pretorius; Werner Israel
texts
eye 25
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Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry that are asymptotic to Minkowski light cones at infinity. We develop the equations of these surfaces and examine their properties. In particular, we show that they are free of caustics for all positive values of the Kerr radial coordinate r. Useful applications include the propagation of high-frequency waves, the definition of Kruskal-like coordinates for a spinning black hole and the characteristic initial-value...
Source: http://arxiv.org/abs/gr-qc/9803080v1
0
0.0
Jun 30, 2018
06/18
by
Houshyar Noshad; Mostafa Honari-Latifpour
texts
eye 0
favorite 0
comment 0
Confinement of single ions in a novel radio-frequency (RF) quadrupole ion trap with spherical shape is investigated. An optimization of this spherical ion trap (SIT) is carried out in order to suppress its nonlinearity substantially by eliminating the electric octupole moment. Hence, a trapping potential and consequently an electric field very similar to the ideal quadrupole ion trap (QIT) are obtained. Afterwards, three stability regions for the optimized SIT are numerically computed. The...
Topics: Physics, Atomic Physics
Source: http://arxiv.org/abs/1411.2204
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28
Sep 20, 2013
09/13
by
Rene Messina
texts
eye 28
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The effects of image charges (i.e., induced surface charges of polarization) in spherical geometry and their implication for charged colloidal systems are investigated. We study analytically and exactly a single microion interacting with a dielectric sphere and discuss the similarities and discrepancies with the case of a planar interface. By means of extensive Monte Carlo (MC) simulations, we study within the framework of the primitive model the effects of image charges on the structure of the...
Source: http://arxiv.org/abs/cond-mat/0204550v4
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50
Sep 20, 2013
09/13
by
Thomas Wiegelmann
texts
eye 50
favorite 0
comment 0
We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherical coordinates. The program uses measured vector magnetograms on the solar photosphere as input and solves the force-free equations in the solar corona. The method is based on an optimization principle and the heritage of the newly developed code is a corresponding method in Cartesian geometry. We test the newly developed code with the help of a semi-analytic solution and rate the...
Source: http://arxiv.org/abs/astro-ph/0612124v1
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115
Jul 20, 2013
07/13
by
Mario Bonk; Alexandre Eremenko
texts
eye 115
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Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan(sqrt 8) ~ 70^\circ 32'. If in addition all critical points of the function are multiple, then a similar statement holds with pi/2. These constants are the best possible. The proof is based on the consideration of negatively curved singular surfaces associated with meromorphic functions.
Source: http://arxiv.org/abs/math/0009251v1
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38
Sep 23, 2013
09/13
by
Eugene B. Kolomeisky; Hussain Zaidi; Luke Langsjoen; Joseph P. Straley
texts
eye 38
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We compute the generic mode sum that quantifies the effect on the spectrum of a harmonic field when a spherical shell is inserted into vacuum. This encompasses a variety of problems including the Weyl spectral problem and the Casimir effect of quantum electrodynamics. This allows us to resolve several long-standing controversies regarding the question of universality of the Casimir self-energy; the resolution comes naturally through the connection to the Weyl problem. Specifically we...
Source: http://arxiv.org/abs/1110.0421v2
An expression is found for the flux due to earthshine incident at any point on a spherical target as a function of target height above ground. Curves showing the variation of reflected signature (or view factor) with observer position and target height are presented for the case of a diffuse target surface. An expression is given for the view factor in the specular case, which is shown to be independent of observer position.
Topics: DTIC Archive, Jordan, Michael P., MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB, *INFRARED...
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34
Sep 19, 2013
09/13
by
Tapan Naskar; Nabajit Chakravarty; Jayanta K. Bhattacharjee; Arnab K. Ray
texts
eye 34
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The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as...
Source: http://arxiv.org/abs/0708.1688v1
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68
Sep 21, 2013
09/13
by
Marissa L. Weichman
texts
eye 68
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This is a missing chapter from Hans Magnus Enzensberger's mathematical adventure The Number Devil (Henry Holt and Company, New York, 1997). In the book, a math-hating boy named Robert is visited in his dreams by the clever Number Devil, who teaches him to love all things numerical. However, we all forget our dreams from time to time. Here is one adventure that Enzensberger overlooked, where the Number Devil introduces Robert to geometry not-of-Euclid, great circles, parallel transport, the...
Source: http://arxiv.org/abs/0706.3342v1
2
2.0
Jun 30, 2018
06/18
by
Jens Oberrath; Ralf Peter Brinkmann
texts
eye 2
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The term Active Plasma Resonance Spectroscopy (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency: A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded, and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature. Based on the cold plasma model,...
Topics: Physics, Plasma Physics
Source: http://arxiv.org/abs/1404.2432
0
0.0
Jun 29, 2018
06/18
by
Mykola I. Sloika; Denis D. Sheka; Volodymyr P. Kravchuk; Oleksandr V. Pylypovskyi; Yuri Gaididei
texts
eye 0
favorite 0
comment 0
Equilibrium magnetization states in thin spherical shells of a magnetically soft ferromagnet are determined by the competition between two interactions: (i) The local exchange interaction favours the more homogeneous onion state with magnetization oriented in meridian directions; such a state is realized in relatively small particles. (ii) The nonlocal magnetostatic interaction prefers the double-vortex configuration with the magnetization oriented in the parallels directions, since it...
Topics: Mesoscale and Nanoscale Physics, Condensed Matter
Source: http://arxiv.org/abs/1609.08555
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34
Sep 18, 2013
09/13
by
Bo Jakobsen; Niels Boye Olsen; Tage Christensen
texts
eye 34
favorite 0
comment 0
We present a novel method of measuring the frequency dependent specific heat at the glass transition applied to 5-polyphenyl-4-ether. The method employs thermal waves effusing radially out from the surface of a spherical thermistor that acts as both a heat generator and thermometer. It is a merit of the method compared to planar effusion methods that the influence of the mechanical boundary conditions are analytically known. This implies that it is the longitudinal rather than the isobaric...
Source: http://arxiv.org/abs/0809.4617v2
228
228
Oct 14, 2008
10/08
by
Charles Davies
texts
eye 228
favorite 0
comment 0
Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.
Source: http://books.google.com/books?id=KwU6mcUtMfwC&oe=UTF-8
188
188
Jan 28, 2008
01/08
by
Albert Ensign Church
texts
eye 188
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comment 0
Book digitized by Google from the library of the University of California and uploaded to the Internet Archive by user tpb.
Source: http://books.google.com/books?id=cyk5AAAAIAAJ&oe=UTF-8
